Spin Responses Of A Superfluid Fermi Gas Of Atoms

The realizition of ultracold Fermi gases of atoms brings a new era to the theoretical and experimental research on degenerate quantum Feimi gases. Since then, Bardeen-Cooper-Schri effer (BCS) condensation of feimionic atoms and Bose-Einstein condensation(BEC) of diatomic molecules of these atoms as well as the BCS-BEC crossover regimes have stimulated a great interest. In this paper we study the dynamic spin responses at finite temperatures in the superfluid state on the BCS side of the BCS-BEC crossover regime.This dissertation is organized as follows. In Chaper I, the preparation of an ultracold Fermi gas of atoms is described. In Chaper II, Feshbach resonance is introduced. The sign of the two body interaction between atoms can be tuned with the magnetic field Feshbach resonance. In Chaper III, by using the path integral representation of the grand partition function, investigate the nature of condensation on the BEC side of the BCS-BEC crossover regime. From the self consistent equations, we have found that BCS condensation of atoms can't occur in such a repulsive two body interaction Fermi gas of atoms. To substantiate our conclusions from the self-consistent equations for the order parameters, the effective atom-atom interaction mediated through molecules has also been computed with the Foldy-Wouthuysen transformation and has been found to be repulsive, which implies the absence of BCS condensation of atoms on the BEC side of the BCS-BEC crossover regime.In Chaper IV, the dynamic spin structure factor at finite temperatures in a superfluid Fermi gas of atoms on the BCS side of the BCS-BEC crossover regime has been studied, it has been found that the dynamic spin structure factor possesses a small peak for frequencies less than twice the energy gap and the peak position dependends on wavevector;the dynamic spin structure factor starts to increase monotomically with frequencies at twice the energy gap. The peak in the dynamic spin structure factor at the finite wavevector implies the possible coexistence of the antiferromagnetic phase with the superfluid phase in ultracold Fermi gases of atoms. This phenomenon has signigicent implications on high temperature superconductivity, since antiferromagnetic spin fluctuation are believed to play an important role in high temperature superconductivity has been under intensive study.